Inverse proportion says

x * y = some constant, for the two variables x and y. (We don't need to know what this constant is, as we'll see below; we just need to know that it doesn't change.)

In our case, x = lumens and y² = distance.

In the first case, x = 200 and y = 3.

In the second case, x = 25, and y = unknown.

Since they have to equal the same constant, given that they have the same inverse ratio, our equation is

200 * 3² = 25 * (distance we want)²

This gives

(Distance we want)² = 72, or

Distance we want = √72 = 6√2